Degree polymerization between crosslinks

A sample of cross-linked natural rubber (polyisoprene) is found to have shear modulus G = 217 kPa at 20 C. Deduce TV, the number of sub-chains between crosslinks per m and hence the number average degree of polymerization between crosslinks. The chemical structure of polyisoprene is given in 3.1. You may take for relative atomic mass C = 12 and H = 1, and for density p = 909 kg/m. Assume... 

The next step in the development of a model is to postulate a perfect network. By definition, a perfect network has no free chain ends. An actual network will contain dangling ends, but it is easier to begin with the perfect case and subsequently correct it to a more realistic picture. We define v as the number of subchains contained in this perfect network, a subchain being the portion of chain between the crosslink points. The molecular weight and degree of polymerization of the chain between crosslinks are defined to be Mj, and n, respectively. Note that these same symbols were used in the last chapter with different definitions. 

The degree of polymerization of the subchain is n. If the degree of polymerization of the molecule as a whole is n, then there are n/n subchains per molecule. We symbolize the number of subchains per molecule as N. Other properties of the subchain-which, incidentally, should not be confused with the chains between crosslink points in elastomers-will also have the subscript s as they emerge. 

Our results show that the network density (vg - 1/Q Q = swelling degree) of the crosslinked polymers is a function of the light intensity, the exposure time, the acrylate content, the molecular weight of the uncrosslinked silicone, and also of the length of the spacer group between the acrylate or methacrylate unit and the silicone backbone. Oxygen influences only the polymerization kinetics, but it does not influence the network density. 

Cuadrado and coworkers have reported the synthesis of polysiloxanes with Fe-Fe bonds using two different methodologies." Polymers with the metal-metal bonds within their backbones (53) were synthesized by polycondensation reactions of disilanols with a dinuclear iron-iron bonded complex, while reaction of a poly-siloxane with Fe(CO)5 resulted in polymer 54. Polymer 54 possessed good thermal stability and poor solubility, which indicates that crosslinking between polymer chains may have occurred. Molecular weight analysis of polymers prepared by polycondensation reactions shows that these polymers have degrees of polymerization between 5 and 10. 

Fig. 7 The relationship between the distribution of the degree of polymerization or crosslink density and the degree of polymerization.

The mesoscale model consists of a set of crosslink nodes (i.e., junctions) connected via single finite-extensible nonlinear elastic (FENE) bonds (that can be potentially cross-linked and/or scissioned), which represent the chain segments between crosslinks. In addition, there is a repulsive Lennard-Jones interaction between all crosslink positions to simulate volume exclusion effects. The Eennard-Jones and FENE interaction parameters were adjusted and the degree of polymerization (p) for a given length of a FENE bond calibrated until the MWD computed from our network matched the experimental MWD of the virgin material [112]. 

Possible morphologies of partially crystalline polymers are shown in Fig. 18. Figure 18a depicts the case of small crystallites that act as physical crosslinks between polymeric chains, thus connecting those chains into a 3-dimensional network. In the case depicted in Fig. 18b, the material forms ribbon-shaped or needle-shaped crystalline regions in which different segments of a large number of chains are incorporated. This could explain the low degree of crystallinity at the LST as detected for the iPP system [80]. 

Chain-growth polymerizations are diffusion controlled in bulk polymerizations. This is expected to occur rapidly, even prior to network development in step-growth mechanisms. Traditionally, rate constants are expressed in terms of viscosity. In dilute solutions, viscosity is proportional to molecular weight to a power that lies between 0.6 and 0.8 (22). Melt viscosity is more complex (23) Below a critical value for the number of atoms per chain, viscosity correlates to the 1.75 power. Above this critical value, the power is nearly 3 4 for a number of thermoplastics at low shear rates. In thermosets, as the extent of conversion reaches gellation, the viscosity asymptotically increases. However, if network formation is restricted to tightly crosslinked, localized regions, viscosity may not be appreciably affected. In the current study, an exponential function of degree of polymerization was selected as a first estimate of the rate dependency on viscosity. 

Polyvinyl alcohol (PVA), which is a water soluble polyhidroxy polymer, is one of the widely used synthetic polymers for a variety of medical applications [197] because of easy preparation, excellent chemical resistance, and physical properties. [198] But it has poor stability in water because of its highly hydrophilic character. Therefore, to overcome this problem PVA should be insolubilized by copolymerization [43], grafting [199], crosslinking [200], and blending [201], These processes may lead a decrease in the hydrophilic character of PVA. Because of this reason these processes should be carried out in the presence of hydrophilic polymers. Polyfyinyl pyrrolidone), PVP, is one of the hydrophilic, biocompatible polymer and it is used in many biomedical applications [202] and separation processes to increase the hydrophilic character of the blended polymeric materials [203,204], An important factor in the development of new materials based on polymeric blends is the miscibility between the polymers in the mixture, because the degree of miscibility is directly related to the final properties of polymeric blends [205],... 

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